Born Dec. 15, 1802, in Kolozsvár (Cluj); died Jan. 27, 1860, in Marosvásárhely (Tirgu-Mureş). Hungarian mathematician.
With N. I. Lobachevskii, Bolyai is one of the creators of non-Euclidean geometry. While still a student at the military Royal Engineering College (in Vienna), Bolyai began to work on a proof of a postulate concerning parallel lines. Upon graduating from the college, he continued intensive work in the same direction. Completing his research, he published it in 1832 in the form of a supplement (Appendix) to the first volume of the works of his father, Farkas Bolyai (1775–1856), professor of mathematics. The exposition of the Appendix is characterized by extreme conciseness and schematism; in the reasoning out of each word and symbol, the Appendix belongs among the most nearly perfect works of mathematical literature. Bolyai’s discoveries did not receive recognition during his lifetime, a fact which had a serious effect on his psyche.
WORKSIn Russian translation:
Appendix: Prilozhenie, soderzhashchee nauku o prostranstve, absoliutno istinnuiu, ne zavisiashchuiu ot istinnosti ili lozhnosti XI aksiomy Evklida (chto a priori nikogda resheno byt’ ne mozhet), c pribavleniem, k sluchaiu lozhnosti, geometricheskoi kvadratury kruga. Moscow-Leningrad, 1950.